Mochizuki's crys-stable bundles: a lexicon and applications

Mochizuki's work on torally crys-stable bundles has extensive implications for the theory of logarithmic connections on vector bundles of rank 2 on curves, once the language is translated appropriately. We describe how to carry out this translation, and give two classes of applications: first, one can conclude almost immediately certain results classifying Frobenius-unstable vector bundles on curves; and second, it follows from prior results of the author that one also obtains results on rational functions with prescribed ramification in positive characteristic.